Question

A half-infinite well has an infinitely high wall at the origin and one of finite height U₀ at x= L . Like the finite well, the number of allowed states is limited. Assume that it has two states, of energy E₁ and E₂ , where E₂ is not much below U₀. Make a sketch of the potential energy, then add plausible sketches of the two allowed wave functions on separate horizontal axes whose heights are E₁ and E₂ .

Short answer

E₁ and E₂ are two states of energy in a half-infinite square well. At a distance of L from the left wall, the right "step" has a height of U₀ .

Step-by-step solution

Given data

Halfway between an infinite square well (potentials on both sides are infinite) and the finite square well lies the half-infinite square well.

Graph for the data

A half-infinite square well with two states of energies and E₁ and E₂ . Here the right "step" has a height of U₀ at a distance L from the left wall. First, we will draw the potential. This is pretty straightforward. "An infinite barrier exists at the origin, followed by a finite barrier at." x= L.

Hence, E₁ and E₂ are two states of energy in a half-infinite square well. At a distance of L from the left wall, the right "step" has a height of U₀ .